1. ENGIN112 L4: Number Codes and Registers ENGIN 112 Intro to Electrical and Computer Engineering Lecture 4 Number Codes and Registers

2. ENGIN112 L4: Number Codes and Registers Overview °2’s complement numbers Addition and subtraction °Binary coded decimal °Gray codes for binary numbers °ASCII characters °Moving towards hardware Storing data Processing data

3. ENGIN112 L4: Number Codes and Registers 2’s Complement Subtraction °Let’s compute (13) 10 - (5) 10. (13) 10 = +(1101) 2 = (01101) 2 (-5) 10 = -(0101) 2 = (11011) 2 °Adding these two 5-bit codes… °Discarding the carry bit, the sign bit is seen to be zero, indicating a correct result. °Numbers in hexadecimal 0 1 1 0 1 +1 1 0 1 1 -------------- 10 1 0 0 0 carry

4. ENGIN112 L4: Number Codes and Registers 2’s Complement Subtraction °Let’s compute (5) 10 – (12) 10. (-12) 10 = -(1100) 2 = (10100) 2 (5) 10 = +(0101) 2 = (00101) 2 °Adding these two 5-bit codes… °Here, there is no carry bit and the sign bit is 1. This indicates a negative result, which is what we expect. (11001) 2 = -(7) 10. °Numbers in hexadecimal 0 0 1 0 1 +1 0 1 0 0 -------------- 1 1 0 0 1

5. ENGIN112 L4: Number Codes and Registers Binary Coded Decimal °Binary coded decimal (BCD) represents each decimal digit with four bits Ex. 0011 0010 1001 = 329 10 °This is NOT the same as 001100101001 2 °Why do this? Because people think in decimal. Digit BCD Code Digit BCD Code 0000050101 1000160110 2001070111 3001181000 4010091001 329

6. ENGIN112 L4: Number Codes and Registers Putting It All Together °BCD not very efficient °Used in early computers (40s, 50s) °Used to encode numbers for seven- segment displays. °Easier to read?

7. ENGIN112 L4: Number Codes and Registers Gray Code °Gray code is not a number system. It is an alternate way to represent four bit data °Only one bit changes from one decimal digit to the next °Useful for reducing errors in communication. °Can be scaled to larger numbers. DigitBinary Gray Code 0 0000 1 0001 2 0010 0011 3 0010 4 0100 0110 5 0101 0111 6 0110 0101 7 0111 0100 8 1000 1100 9 1001 1101 10 1010 1111 11 1011 1110 12 1100 1010 13 1101 1011 14 1110 1001 15 1111 1000

8. ENGIN112 L4: Number Codes and Registers ASCII Code °American Standard Code for Information Interchange °ASCII is a 7-bit code, frequently used with an 8 th bit for error detection (more about that in a bit). CharacterASCII (bin) ASCII (hex) DecimalOctal A10000014165101 B10000104266102 C10000114367103 … Z a … 1 ‘

9. ENGIN112 L4: Number Codes and Registers ASCII Codes and Data Transmission °ASCII Codes °A – Z (26 codes), a – z (26 codes) °0-9 (10 codes), others (@#$%^&*….) °Complete listing in Mano text °Transmission susceptible to noise °Typical transmission rates (1500 Kbps, 56.6 Kbps) °How to keep data transmission accurate?

10. ENGIN112 L4: Number Codes and Registers Parity Codes °Parity codes are formed by concatenating a parity bit, P to each code word of C. °In an odd-parity code, the parity bit is specified so that the total number of ones is odd. °In an even-parity code, the parity bit is specified so that the total number of ones is even. Information BitsP 1 1 0 0 0 0 1 1  Added even parity bit 0 1 0 0 0 0 1 1  Added odd parity bit

11. ENGIN112 L4: Number Codes and Registers Parity Code Example °Concatenate a parity bit to the ASCII code for the characters 0, X, and = to produce both odd-parity and even-parity codes. CharacterASCII Odd-Parity ASCII Even-Parity ASCII 001100001011000000110000 X10110000101100011011000 =01111001011110000111100

12. ENGIN112 L4: Number Codes and Registers Binary Data Storage Binary cells store individual bits of data Multiple cells form a register. Data in registers can indicate different values Hex (decimal) BCD ASCII Binary Cell 00101011

13. ENGIN112 L4: Number Codes and Registers Register Transfer °Data can move from register to register. °Digital logic used to process data °We will learn to design this logic Register ARegister B Register C Digital Logic Circuits

14. ENGIN112 L4: Number Codes and Registers Transfer of Information °Data input at keyboard °Shifted into place °Stored in memory NOTE: Data input in ASCII

15. ENGIN112 L4: Number Codes and Registers Building a Computer °We need processing °We need storage °We need communication °You will learn to use and design these components.

16. ENGIN112 L4: Number Codes and Registers Summary °Although 2’s complement most important, other number codes exist °ASCII code used to represent characters (including those on the keyboard) °Registers store binary data °Next time: Building logic circuits!